Algebraic Decoding of Negacyclic Codes over Z4
Résumé
We investigate Berlekamp's negacyclic codes and discover that these codes, when considered over the integers modulo 4, do not su er any of the restrictions on the minimum distance observed in Berlekamp's original papers [2, 3]. We present an algebraic decoding algorithm for this class of codes that corrects any error pattern of Lee weight t. Our treatment uses Grobner bases, the decoding complexity is quadratic in t.
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